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Mappings Between Surfaces

In: New Foundations in Mathematics

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  • Garret Sobczyk

    (Universidad de Las Américas, Departamento de Física y Matemáticas)

Abstract

In this chapter we explore when a mapping will preserve geodesics, the shortest distances between two points on a surface, and when a mapping will preserve the angles between the intersection of two curves on the surface, known as conformal mappings. A conformal mapping of a pseudo-Euclidean space $${\mathbb{R}}^{p,q}$$ generalizes the idea of an analytic function in the two-dimensional theory of complex variables.

Suggested Citation

  • Garret Sobczyk, 2013. "Mappings Between Surfaces," Springer Books, in: New Foundations in Mathematics, edition 127, chapter 0, pages 275-295, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-8385-6_16
    DOI: 10.1007/978-0-8176-8385-6_16
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